|
Search: id:A083102
|
|
|
| A083102 |
|
a(n)=2a(n-1)+10*a(n-2). |
|
+0
5
|
|
| 1, 2, 14, 48, 236, 952, 4264, 18048, 78736, 337952, 1463264, 6306048, 27244736, 117549952, 507547264, 2190594048, 9456660736, 40819261952, 176205131264, 760602882048, 3283257076736, 14172542973952, 61177656715264
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
a(n+1)=a(n)+A083101(n). A083101(n)/a(n) converges to sqrt(11).
Generalized Pell numbers (A000129).Anti-diagonals of A038207 [From M. Dols (markdols99(AT)yahoo.com), Aug 31 2009]
|
|
FORMULA
|
G.f.: 1/(1-2x-10x^2)
E.g.f. : exp(x)sinh(sqrt(11)x)/sqrt(11); a(n)=sum{k=0..n, binomial(n, 2k+1)11^k}. - Paul Barry (pbarry(AT)wit.ie), Sep 29 2004
a(n)=((1+sqrt(11))^n-(1-sqrt(11))^n)/(2*sqrt(11)) [From Rolf Pleisch (r_pleisch(AT)gmx.ch), Jul 06 2009]
|
|
MATHEMATICA
|
CoefficientList[Series[1/(1-2x-10x^2), {x, 0, 25}], x]
|
|
PROGRAM
|
(Other) sage: [lucas_number1(n, 2, -10) for n in xrange(1, 24)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
|
|
CROSSREFS
|
Sequence in context: A085929 A036659 A079937 this_sequence A056080 A163796 A153978
Adjacent sequences: A083099 A083100 A083101 this_sequence A083103 A083104 A083105
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Mario Catalani (mario.catalani(AT)unito.it), Apr 22 2003
|
|
|
Search completed in 0.002 seconds
|
